The present invention relates to information storage systems and, more particularly, to control of characteristics of the data retrieval channel through which data is retrieved from storage in such systems.
Digital data magnetic recording systems store digital data by recording same in a moving magnetic media layer using a storage, or "write", electrical current-to-magnetic field transducer, or "head", positioned immediately adjacent thereto. The data is stored or written to the magnetic media by switching the direction of flow in an otherwise substantially constant magnitude write current that is established in coil windings in the write transducer in accordance with the data. Each write current direction transition results in a reversal of the magnetization direction, in that portion of the magnetic media just then passing by the transducer during this directional switching of the current flow, with respect to the magnetization direction in that media induced by the previous in the opposite direction. In one recording scheme, often termed nonreturn-to-zero inverted (NRZI), each magnetization direction reversal occurring over a short portion of the magnetic media moving past the transducer represents a binary number system digit "1", and the lack of any such reversals in that portion represents a binary digit "0".
Recovery of such recorded digital data is accomplished through positioning a retrieval, or "read" magnetic field-to-voltage transducer, (which may be the same as the storage transducer if both of these transducers rely on inductive coupling between the media fields and the transducer) or "head", is positioned to have the magnetic media, containing previously stored data, pass thereby. Such passing by of the media adjacent to the transducer permits the flux accompanying the magnetization reversal regions in that media either to induce a corresponding voltage pulse in forming an analog output read signal for that retrieval transducer or, alternatively, change a transducer circuit parameter to thereby provide such an output signal voltage pulse. In the coding scheme described above, each such voltage pulse in the read transducer output signal due to the reversal of magnetization directions between adjacent media portions is taken to represent a binary digit "1", and the absence of such a pulse in corresponding media portions is taken to represent a binary digit "0".
Digital data magnetic recording systems have used peak detection methods for the detection of such voltage pulses in the retrieved analog signal as the basis for digitizing this signal. Such methods are based on determining which peaks in that signal exceed a selected threshold to determine that a binary digit "1" related pulse occurred in the retrieved signal, and also use the times between those voltage pulses to reconstruct the timing information used in the preceding recording operation in which the data were stored in the magnetic media as described above. The analog retrieved signal is provided to a phase-locked loop forming a controlled oscillator, or a phase-lock oscillator or synchronizer, which produces an output timing signal, or "clock" signal from the positions of the detected peaks in this analog retrieved signal. Absolute time is not used in operating the data retrieval system portion since the speed of the magnetic media varies over time during both the storage operation and the retrieval operation to result in nonuniform time intervals, or nonuniform multiples thereof, occurring between the voltage pulses in the analog retrieved signal.
There is always a desire in magnetic recording systems to devote less of the magnetic media along a track therein to the storage of a bit to thereby permit increasing the density of the bits stored. The use of peak detection places a limit on the density of bits along a track because increasing that density beyond some point will lead to too much intersymbol interference which in turn leads to errors in the recovery of data using such peak detection methods. Because of this limit, recent increases in bit density along a track in a magnetic media have come with the acceptance of a controlled, or known, amount of intersymbol interference which, since known, allows detection of the pulses involved despite this interference. The read transducer analog output signal generated from the binary bits or symbols stored in the magnetic media is sampled with the resulting samples being converted to digital data, and the samples are taken at a rate which leads to more than one sample per pulse rather than the single sample per pulse which would be sufficient for peak detection if sampling was used therewith. Since each individual sample reflects only part of the pulse response, this process used in a system results in referring to such a system as a partial response system.
A digital data magnetic recording system comprises a bandpass data retrieval channel in that it is unable to transmit very low frequencies, and has an upper frequency beyond which its transmission is also quite poor. Although there are a number of possible alternative partial response system arrangements, there is substantial value in matching the partial response spectrum to that expected for the data to be transmitted in the channel. A relatively simple partial response system that does not require transmission at very low frequencies is known as a class 4 partial response system, and is typically used in magnetic digital data recording systems. Such a response is obtained by providing an overall channel and filter response equal to that of the sum of two opposite polarity Nyquist channel impulse responses separated in time by two sample intervals. Such an arrangement will lead to a filter analog output signal from which ideally can be obtained three alternative possible sample values of -1, 0 and 1 for an input signal based on binary recorded data if sampled at appropriate instants. The sequence of resulting samples can be viewed as comprising an interleaving of two subsequences, one formed of the odd numbered samples and the other formed of the even numbered samples, in view of each sample value having contributions from only the currently retrieved stored datum and second preceding datum.
A read transducer analog output signal provided through any kind of a data retrieval channel is subject to containing errors therein as a result due to noise, timing errors, gain errors, signal offset, channel nonlinearities such as asymmetry, and the like encountered in the course of retrieval- Linear equalization is used in such a channel to provide a frequency response suited for a class 4 partial response channel and to counter linear distortions which would otherwise be imposed on the channel output waveform but cannot counter nonlinear distortions. One such nonlinear distortion in a read channel is asymmetry in the channel response to the binary input values of "0" and "1". One typical source of such asymmetry in a read channel occurs with the use of a magnetoresistive transducer in the read head which often provides a different magnitude output when reading a magnetization transition from the magnetic media in going from a first state to an opposite state than when making a transition from an alternative second state to an opposite state.
Feedback control systems are typically used to control the characteristics of data retrieval channels through estimating the errors with respect to desired values in the channel gain, signal offset and sampling timing phase errors and attempting to drive such errors to zero. Such systems which fail to compensate for channel asymmetry either suffer an undesirable introduction of bias in the estimates or an increase the variance of those estimates over what they would be in the absence of such asymmetry. This result can be shown in connection with the data retrieval portion of a magnetic media digital data storage system shown in block diagram form in FIG. 1.
In that figure, a magnetic material covered disc, 10, containing pluralities of magnetization direction reversals along each of a plurality of more or less concentric, circular tracks, is rotated past a data retrieval transducer arrangement, 11, or "read head", positioned adjacent a selected track by a "head" positioner and initial signal processor, 12, about a spindle, 13, to provide an initial analog read signal, x(t). This signal is subjected to further processing in a signal processing block, 14, including linear channel equalization. The output from signal processing block 14 is an analog output signal, y(t), which is provided to a variable gain amplifier, 15, and then this signal as amplified, is provided to a signal offset compensation adder, 16. The output of this adder is then provided to a sampler, 17, based on a sample and hold circuit which is operated by a sample acquisition timing signal provided by signal processing block 14 that is derived from the samples provided by sampler 17 to that signal processing block.
Consider the received signal y(t) from the data retrieval channel equalizer in a channel subject to an asymmetry nonlinearity which comes about because of input analog signal x(t), obtained from the data stored in the magnetic media, being introduced into the class 4 partial response channel with a nonlinear element or elements therein. Such a channel output signal can then be approximated to reflect the nonlinearity as EQU y(t)=x(t)-c.sub.asymm x.sup.2 (t).
As seen in the system block diagram shown in FIG. 1, this signal is then subjected to a controlled gain in amplifier 15 and to controlled offset compensation in adder 16, and thereafter presented to sampler 17 to be sampled over time in each successive sampling interval T therein to provide samples y(kT) for use in further signal processing steps with k being a counting integer. If the values of the channel input signal x(t) at sampling times kT are written x(kT), the normalized versions thereof are defined as x[k] and are expected to take the values 1, 0 or -1 as described above. In the circumstance of the gain being 1 and the offset being 0, the above equation indicates that the samples y[kT] will take the values 1-c.sub.asymm, 0 or -1-c.sub.asymm using the normalized values for input signal x(t)at the sampling instants. However, the signal presented to sampler 17 is corrupted by noise present at the sample instants represented by n[kT]. Such noise samples can be considered independent random variables at each sampling instant having a mean value of zero and a variance of .sigma..sup.2.
Furthermore, the signal is also corrupted by signal offset acquired in the channel, then amplified in amplifier 15, and subjected to signal offset compensation in adder 16. Assuming that the timing phase errors have been eliminated in block 14, the value of a sample taken at kT will instead of being y[kT], be EQU s[kT]=s[k]=g[k]{y(kT)+n(kT)}+c.sub.offset (kT)+.delta.[k],
where the proper gain g[k]=g[kT] for the channel and the needed offset compensation o[k]=o[kT] for the channel are to be estimated.
The error e[k]=e[kT] in this sample is then defined as the difference between the sample magnitude value and the anticipated or expected value for that sample, or EQU e[k]=s[k]-p.sub.x[k].
The expected values of s[k] are, in general, denoted p.sub.x[k] for a particular value of the input signal and are specifically written as p.sub.1. p.sub.0 and p.sub.-1. They can be defined as
p.sub.1 .DELTA. anticipated value of samples corresponding to x[k]=1, PA1 p.sub.0 .DELTA.anticipated value of samples corresponding to x[k]=0, and PA1 p.sub.-1 .DELTA. anticipated value of samples corresponding to x[k]-1.
In typical feedback control loops for class 4 partial response data retrieval channels, asymmetry is disregarded and the values for use in those loops are taken as p.sub.1 =1, p.sub.0 =0 and P.sub.-1 =-1. In an alternative that provides some recognition of asymmetry, these expected values are taken instead to be p.sub.1 =1, p.sub.0 =0 and p.sub.-1 =-V.sub.n with V.sub.n being a programmable value which is estimated in an external channel assessment arrangement and inserted for use in the control loops by intervention of a microprocessorserving as the overall system controller.
Class 4 partial response data retrieval channels are desirably operated to minimize the mean square error resulting from the error source sought to be controlled. Such an effort requires finding the error gradient of this mean squared error which must be set to zero and solved. The difficulties in finding the minimum mean squared error leads to instead using the error gradient of the squared error itself as a basis for adaptively adjusting the error toward a minimum without having to find a mean value. This results in a stochastic gradient which is used for the adjusting the parameter giving rise to the error or a compensator countering such an error in a direction opposite the error direction in a feedback loop. The stochastic gradient of the squared error with respect to the signal offset estimator ignoring asymmetry is ##EQU1## Since this gradient is integrated over time and the result multiplied by a small step size factor for loop stability to provide the signal to control an offset compensation adder, the factor 2 can in effect be included in the step size factor. Thus, controlling error due to signal offset is based on a feedback loop forcing the error to zero.
This is accomplished in the system of FIG. 1 by using a pair of comparators, 20 and 21, and a source of threshold values, 22, to determine whether sample values from sampler 17 are likely to have been intended to have a value of 1, 0 or -1, and using that determination to provide an expected value for the corresponding sample from a source, 23, to a subtractor, 24. Each sample form sampler 17 is provided to the non-inverting input of comparator 20, the inverting input of comparator 21, and to one input of subtractor 24. A positive threshold value of one half is provided by source 22 to the inverting input of comparator 20 and a further threshold value of negative one half is supplied by source 22 to the non-inverting input of comparator 21. Samples with values larger than one half cause comparator 20 to switch its output from a "0" logic state value to a "1" logic state value and leave a "0" logic state value at the output of comparator 21. This causes a switch, 25, to close to provide the expected sample value of 1, supplied by source 23, to the input of subtractor 24.
A sample value that is less than negative one half provides the opposite result in logic states at the outputs of comparators 20 and 21. Such a condition instead causes a switch, 26, to close to provide the expected sample value of -1, supplied by source 23, to the input of subtractor 24. If the absolute value of the sample is less than one half, a "0" logic state value appears at the outputs of both of comparators 20 and 21. In this situation only, a NOR gate, 27, having two inputs, each being connected to a corresponding one of the outouts of comparators 20 and 21, will have its output go from a "0" logic state value to a "1" logic state value to thereby close a further switch, 28. This results in the providing the expected sample value of 0, supplied by source 23, to the input of subtractor 24. The expected sample value selected by one of switches 25, 26 and 28 to be provided to one of the inputs of subtractor 24 is subtracted therein from the corresponding sample value in the sequence thereof provided to the other input of that subtractor to yield the corresponding sample error e[k] in the sequence thereof at the subtractor output.
A fractional step size factor is applied in a step size box, 29, to this error as necessary for loop stability and the sequence of errors so formed in this manner is integrated over time in a time integrator, or analog value summer, 30. The output signal of integrator 30 is then supplied to offset compensation adder 16 to act toward cancelling the signal offset in the amplified linear equalizer output signal supplied from signal processing block 14.
The stochastic gradient of the squared error with respect to gain error estimator ignoring asymmetry is ##EQU2## after substituting the expected input signal value at sampling for the actual sample value in the second factor. Again, since this gradient is integrated over time and the result multiplied by a small step size factor for loop stability to provide the signal to control a variable gain amplifier, the factor 2 can in effect be included in the step size factor. Hence, controlling error due to gain variation is based on a feedback loop forcing the product of the error and the expected channel input signal value at sampling instants to zero.
This is accomplished in the system of FIG. 1 by use of a further set of three switches, 31, 32 and 33, to selectively transfer a version of the error provided at the output of subtractor 24 to a further step size block, 34, to apply a fractional step size factor for loop stability. Switch 31 is controlled by the same signal as switch 25, and so transmits the error unchanged if the sample value exceeded one half to thus behave as though transmitting the error multiplied by the expected input signal value at sampling of 1. Similarly, Switch 32 is controlled by the same signal as switch 26, and so permits transmission if the sample value was less than negative one half, but only after the error has passed through an analog inverter, 35, to change its algebraic sign, to thus behave as though transmitting the error multiplied by the expected input signal value at sampling of -1. Finally, switch 33 is controlled by the same signal as switch 28, but transmits the expected value of zero supplied from source 23 if the sample absolute value was less than one half, to thus behave as though transmitting the error multiplied by the expected input signal value at sampling of 0.
The effective error and expected input signal value product signal provided to step size block 34 has a fractional step size applied to it in that block which transmits the result to a time integrator, or analog value summer, 36. The resulting signal is provided to the gain control input of variable gain amplifier 15 to control the amplification of the channel signal supplied to the signal input of amplifier 15 by signal processing block 14.
Although the feedback loops just described in connection with the system of FIG. 1 ignore asymmetry in the design thereof, the asymmetry actually present in the data retrieval channel nevertheless affects the behavior of these loops. As described above, the loops act to force the corresponding gradients to zero resulting, for the signal offset control loop, in having the expected value of the corresponding gradient be zero, or EQU E{.gradient.o[k]}=E{e[k]}=0.
If the probability of an input signal value at sampling of 1 is P(1), the probability of an input signal value at sampling of 0 is P(0) and the probability of an input signal value at sampling of -1 is P(-1), this expectation can be written as ##EQU3## for the noise having a zero mean. Setting this result to zero as indicated above results in showing the offset compensator will introduce into the signal offset compensation loop the value ##EQU4## to result in a asymmetry based bias value added in the resulting compensation.
Forcing the gain gradient to zero results in having the expected value of that gradient, in the gain control loop, being zero, or EQU E{.gradient.g}=E{x[k]e[k]}=0.
This expectation can be written as ##EQU5## Since P(1)=P(-1), EQU E{x[k]e[k]}=g[k][P(1)+P(-1)]-P(1)-P(-1).
Setting this result to zero as indicated above results in showing the loop forces the gain to a normalized gain value of 1, that is g.fwdarw.1. Thus, the gain control loop results in an unbiased normalized gain despite the asymmetry present in the data retrieval channel.
However, this asymmetry introduces an increased variance in the gain control loop. Since the expected value of the gain gradient is forced to be zero by the gain control loop, the variance for the gain gradient is ##EQU6## If the gain control loop has forced the normalized gain to 1 and the signal offset control loop has forced the offset compensation to the value given above, this becomes ##EQU7## which, for the noise being of zero mean value with a variance of .sigma..sup.2, gives ##EQU8## Thus, the presence of a term involving the asymmetry coefficient indicates an increase in the variance of the gain gradient due to asymmetry in the data retrieval channel.
Although the variance due to noise can be halved by using the two most recent gain gradient values in a two point moving average estimate, the asymmetry contribution to the gain gradient variance remains present in a pattern dependent manner. Successive positive and negative valued samples as the basis for the moving average estimate will tend to cancel the asymmetry contribution to the gain gradient variance, but other data patterns will continue to contribute to that variance. Thus, there is a desire for a digital data retrieval channel characteristics control system to provide more nearly optimal channel gain and signal offset performance in the presence of channel asymmetry. Furthermore, there is a desire to provide such a control system in an all, or nearly all, analog form to avoid needing to provide digital registers for this purpose and the corresponding operating delays and increase in power consumption.